digitaldeath

Thanks.
Here’s my implemented solution:

// Get the names (terms) of all departments
    $terms = get_terms("departments");

    // How many departments?
    $count = count($terms);

    if ($count > 0) {
        $div_counter = 0;

        // For each department, do the following
        foreach ($terms as $term) {

            // We don't want to generate duplicate output for certain departments, so we filter those out.
            if (($term->slug != 'executive-board') && ($term->slug != 'scientific-and-technical-board') &&
                ($term->slug != 'managers'))
            {

                // Determine if this section should be placed in the left or right column

                $div_counter += 1;
                if (($div_counter % 2) == 1) { // Odd number - right column
                    ?><div class="people-right-column"><?php

                } else {
                    ?><div class="people-left-column"><?php  // Even number - left column
                }

                // Print the department name
                echo "<h4 class=\"dept-title\">" . $term->name . "</h4>";

                // Check to see what posts are tagged with the current department name (term) - the current department name is known as we're inside the loop here.
                $args = array('post_type' => 'people', 'taxonomy' => 'departments', 'term' => $term->name, 'posts_per_page' => -1, 'orderby' => 'menu_order', 'order' => 'ASC');
                $loop = new WP_query($args);

                // While there are posts within the current department term, do something with the post (display required information etc.)
                while ($loop->have_posts()) : $loop->the_post();
                    ?>
                    <div class="profile-preview">

                        <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a> (<?php the_field('title'); ?>)
                        <?php
                             the_excerpt();
                        ?>
                    </div>
                        <?php endwhile; ?></div><?php
            }
        }
    }
?>